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Full text of "Analytical Mechanics"

Therefore
83
Thus the particle describes a circle with a constant speed ka.   The direction of the velocity at any instant is given by the relation
tan 0 = K
x
The components vr and vp may be obtained at once by remembering, (1) that the radius vector is constant: e.g., f = 0, (2) that it is always normal to the path: e.g., rdB = ds. Therefore
and
82.  Velocity of a Particle Relative to Another Particle in Motion.—Consider the motion of a particle Pi, Fig. 52, with
O
Fro. 52.
respect to a particle P2, when both are in motion relative to the system of axes XOY.
Let the system of axes X'PiY' have P2 for its origin and move with its axes parallel to those of the system XOY. Further let (xi, j/i) and (x2? y2) be the positions, and YI and v2 the velocities of PI and P2 with respect to XOY. Then